Fibonacci.js overhaul (TheAlgorithms#1049)

Rudxain · web-flow · commit 1b64ba68fa08 · 2022-06-27T10:09:54.000+05:30
diff --git a/Maths/Fibonacci.js b/Maths/Fibonacci.js
@@ -1,51 +1,67 @@
-const list = []
-
-const FibonacciIterative = (nth) => {
-  const sequence = []
-
-  if (nth >= 1) sequence.push(1)
-  if (nth >= 2) sequence.push(1)
-
-  for (let i = 2; i < nth; i++) {
-    sequence.push(sequence[i - 1] + sequence[i - 2])
+// https://en.wikipedia.org/wiki/Generalizations_of_Fibonacci_numbers#Extension_to_negative_integers
+const FibonacciIterative = (num) => {
+  const isNeg = num < 0
+  if (isNeg) num *= -1
+  const sequence = [0]
+
+  if (num >= 1) sequence.push(1)
+  if (num >= 2) sequence.push(isNeg ? -1 : 1)
+
+  for (let i = 2; i < num; i++) {
+    sequence.push(
+      isNeg ? sequence[i - 1] - sequence[i] : sequence[i] + sequence[i - 1]
+    )
   }
 
   return sequence
 }
 
-const FibonacciRecursive = (number) => {
+const FibonacciGenerator = function * (neg) {
+  let a = 0
+  let b = 1
+  yield a
+  while (true) {
+    yield b;
+    [a, b] = neg ? [b, a - b] : [b, a + b]
+  }
+}
+
+const list = []
+const FibonacciRecursive = (num) => {
+  const isNeg = num < 0
+  if (isNeg) num *= -1
   return (() => {
     switch (list.length) {
       case 0:
-        list.push(1)
-        return FibonacciRecursive(number)
+        list.push(0)
+        return FibonacciRecursive(num)
       case 1:
         list.push(1)
-        return FibonacciRecursive(number)
-      case number:
+        return FibonacciRecursive(num)
+      case num + 1:
         return list
       default:
-        list.push(list[list.length - 1] + list[list.length - 2])
-        return FibonacciRecursive(number)
+        list.push(list.at(-1) + list.at(-2))
+        return FibonacciRecursive(num)
     }
-  })()
+  })().map((fib, i) => fib * (isNeg ? (-1) ** (i + 1) : 1))
 }
 
 const dict = new Map()
-
 const FibonacciRecursiveDP = (stairs) => {
-  if (stairs <= 0) return 0
-  if (stairs === 1) return 1
+  const isNeg = stairs < 0
+  if (isNeg) stairs *= -1
+
+  if (stairs <= 1) return stairs
 
   // Memoize stair count
-  if (dict.has(stairs)) return dict.get(stairs)
+  if (dict.has(stairs)) return (isNeg ? (-1) ** (stairs + 1) : 1) * dict.get(stairs)
 
-  const res =
-    FibonacciRecursiveDP(stairs - 1) + FibonacciRecursiveDP(stairs - 2)
+  const res = FibonacciRecursiveDP(stairs - 1) + FibonacciRecursiveDP(stairs - 2)
 
   dict.set(stairs, res)
 
-  return res
+  return (isNeg ? (-1) ** (stairs + 1) : 1) * res
 }
 
 // Algorithms
@@ -59,12 +75,16 @@ const FibonacciRecursiveDP = (stairs) => {
 // a function of the number of input bits
 // @Satzyakiz
 
-const FibonacciDpWithoutRecursion = (number) => {
-  const table = []
+const FibonacciDpWithoutRecursion = (num) => {
+  const isNeg = num < 0
+  if (isNeg) num *= -1
+  const table = [0]
   table.push(1)
-  table.push(1)
-  for (let i = 2; i < number; ++i) {
-    table.push(table[i - 1] + table[i - 2])
+  table.push(isNeg ? -1 : 1)
+  for (let i = 2; i < num; ++i) {
+    table.push(
+      isNeg ? table[i - 1] - table[i] : table[i] + table[i - 1]
+    )
   }
   return table
 }
@@ -76,24 +96,31 @@ const copyMatrix = (A) => {
 }
 
 const Identity = (size) => {
+  const isBigInt = typeof size === 'bigint'
+  const ZERO = isBigInt ? 0n : 0
+  const ONE = isBigInt ? 1n : 1
+  size = Number(size)
   const I = Array(size).fill(null).map(() => Array(size).fill())
   return I.map((row, rowIdx) => row.map((_col, colIdx) => {
-    return rowIdx === colIdx ? 1 : 0
+    return rowIdx === colIdx ? ONE : ZERO
   }))
 }
 
 // A of size (l x m) and B of size (m x n)
-// product C will be of size (l x n)
+// product C will be of size (l x n).
+// both matrices must have same-type numeric values
+// either both BigInt or both Number
 const matrixMultiply = (A, B) => {
   A = copyMatrix(A)
   B = copyMatrix(B)
+  const isBigInt = typeof A[0][0] === 'bigint'
   const l = A.length
   const m = B.length
   const n = B[0].length // Assuming non-empty matrices
   const C = Array(l).fill(null).map(() => Array(n).fill())
   for (let i = 0; i < l; i++) {
     for (let j = 0; j < n; j++) {
-      C[i][j] = 0
+      C[i][j] = isBigInt ? 0n : 0
       for (let k = 0; k < m; k++) {
         C[i][j] += A[i][k] * B[k][j]
       }
@@ -110,18 +137,25 @@ const matrixMultiply = (A, B) => {
 // A is a square matrix
 const matrixExpo = (A, n) => {
   A = copyMatrix(A)
+  const isBigInt = typeof n === 'bigint'
+  const ZERO = isBigInt ? 0n : 0
+  const TWO = isBigInt ? 2n : 2
 
   // Just like Binary exponentiation mentioned in ./BinaryExponentiationIterative.js
-  let result = Identity(A.length) // Identity matrix
-  while (n > 0) {
-    if (n % 2 !== 0) result = matrixMultiply(result, A)
-    n = Math.floor(n / 2)
-    if (n > 0) A = matrixMultiply(A, A)
+  let result = Identity((isBigInt ? BigInt : Number)(A.length)) // Identity matrix
+  while (n > ZERO) {
+    if (n % TWO !== ZERO) result = matrixMultiply(result, A)
+    n /= TWO
+    if (!isBigInt) n = Math.floor(n)
+    if (n > ZERO) A = matrixMultiply(A, A)
   }
   return result
 }
 
-const FibonacciMatrixExpo = (n) => {
+const FibonacciMatrixExpo = (num) => {
+  const isBigInt = typeof num === 'bigint'
+  const ZERO = isBigInt ? 0n : 0
+  const ONE = isBigInt ? 1n : 1
   // F(0) = 0, F(1) = 1
   // F(n) = F(n-1) + F(n-2)
   // Consider below matrix multiplication:
@@ -134,23 +168,28 @@ const FibonacciMatrixExpo = (n) => {
   // or                  F(n, n-1) = A * A * F(n-2, n-3)
   // or                  F(n, n-1) = pow(A, n-1) * F(1, 0)
 
-  if (n === 0) return 0
+  if (num === ZERO) return num
+
+  const isNeg = num < 0
+  if (isNeg) num *= -ONE
 
   const A = [
-    [1, 1],
-    [1, 0]
+    [ONE, ONE],
+    [ONE, ZERO]
   ]
-  const poweredA = matrixExpo(A, n - 1) // A raised to the power n-1
+
+  const poweredA = matrixExpo(A, num - ONE) // A raised to the power n-1
   let F = [
-    [1],
-    [0]
+    [ONE],
+    [ZERO]
   ]
   F = matrixMultiply(poweredA, F)
-  return F[0][0]
+  return F[0][0] * (isNeg ? (-ONE) ** (num + ONE) : ONE)
 }
 
 export { FibonacciDpWithoutRecursion }
 export { FibonacciIterative }
+export { FibonacciGenerator }
 export { FibonacciRecursive }
 export { FibonacciRecursiveDP }
 export { FibonacciMatrixExpo }
diff --git a/Maths/test/Fibonacci.test.js b/Maths/test/Fibonacci.test.js
@@ -2,30 +2,61 @@ import {
   FibonacciDpWithoutRecursion,
   FibonacciRecursiveDP,
   FibonacciIterative,
+  FibonacciGenerator,
   FibonacciRecursive,
   FibonacciMatrixExpo
 } from '../Fibonacci'
 
 describe('Fibonacci', () => {
   it('should return an array of numbers for FibonacciIterative', () => {
-    expect(FibonacciIterative(5)).toEqual(
-      expect.arrayContaining([1, 1, 2, 3, 5])
+    expect(FibonacciIterative(6)).toEqual(
+      expect.arrayContaining([0, 1, 1, 2, 3, 5, 8])
+    )
+    expect(FibonacciIterative(-6)).toEqual(
+      expect.arrayContaining([0, 1, -1, 2, -3, 5, -8])
     )
   })
 
+  it('should return number for FibonacciGenerator', () => {
+    const positive = FibonacciGenerator()
+    expect(positive.next().value).toBe(0)
+    expect(positive.next().value).toBe(1)
+    expect(positive.next().value).toBe(1)
+    expect(positive.next().value).toBe(2)
+    expect(positive.next().value).toBe(3)
+    expect(positive.next().value).toBe(5)
+    expect(positive.next().value).toBe(8)
+
+    const negative = FibonacciGenerator(true)
+    expect(negative.next().value).toBe(0)
+    expect(negative.next().value).toBe(1)
+    expect(negative.next().value).toBe(-1)
+    expect(negative.next().value).toBe(2)
+    expect(negative.next().value).toBe(-3)
+    expect(negative.next().value).toBe(5)
+    expect(negative.next().value).toBe(-8)
+  })
+
   it('should return an array of numbers for FibonacciRecursive', () => {
-    expect(FibonacciRecursive(5)).toEqual(
-      expect.arrayContaining([1, 1, 2, 3, 5])
+    expect(FibonacciRecursive(6)).toEqual(
+      expect.arrayContaining([0, 1, 1, 2, 3, 5, 8])
+    )
+    expect(FibonacciRecursive(-6)).toEqual(
+      expect.arrayContaining([-0, 1, -1, 2, -3, 5, -8])
     )
   })
 
   it('should return number for FibonacciRecursiveDP', () => {
-    expect(FibonacciRecursiveDP(5)).toBe(5)
+    expect(FibonacciRecursiveDP(6)).toBe(8)
+    expect(FibonacciRecursiveDP(-6)).toBe(-8)
   })
 
   it('should return an array of numbers for FibonacciDpWithoutRecursion', () => {
-    expect(FibonacciDpWithoutRecursion(5)).toEqual(
-      expect.arrayContaining([1, 1, 2, 3, 5])
+    expect(FibonacciDpWithoutRecursion(6)).toEqual(
+      expect.arrayContaining([0, 1, 1, 2, 3, 5, 8])
+    )
+    expect(FibonacciDpWithoutRecursion(-6)).toEqual(
+      expect.arrayContaining([0, 1, -1, 2, -3, 5, -8])
     )
   })
 
@@ -36,5 +67,32 @@ describe('Fibonacci', () => {
     expect(FibonacciMatrixExpo(3)).toBe(2)
     expect(FibonacciMatrixExpo(4)).toBe(3)
     expect(FibonacciMatrixExpo(5)).toBe(5)
+    expect(FibonacciMatrixExpo(6)).toBe(8)
+
+    expect(FibonacciMatrixExpo(-0)).toBe(-0)
+    expect(FibonacciMatrixExpo(-1)).toBe(1)
+    expect(FibonacciMatrixExpo(-2)).toBe(-1)
+    expect(FibonacciMatrixExpo(-3)).toBe(2)
+    expect(FibonacciMatrixExpo(-4)).toBe(-3)
+    expect(FibonacciMatrixExpo(-5)).toBe(5)
+    expect(FibonacciMatrixExpo(-6)).toBe(-8)
+  })
+
+  it('should return bigint for FibonacciMatrixExpo', () => {
+    expect(FibonacciMatrixExpo(0n)).toBe(0n)
+    expect(FibonacciMatrixExpo(1n)).toBe(1n)
+    expect(FibonacciMatrixExpo(2n)).toBe(1n)
+    expect(FibonacciMatrixExpo(3n)).toBe(2n)
+    expect(FibonacciMatrixExpo(4n)).toBe(3n)
+    expect(FibonacciMatrixExpo(5n)).toBe(5n)
+    expect(FibonacciMatrixExpo(6n)).toBe(8n)
+
+    expect(FibonacciMatrixExpo(-0n)).toBe(0n)
+    expect(FibonacciMatrixExpo(-1n)).toBe(1n)
+    expect(FibonacciMatrixExpo(-2n)).toBe(-1n)
+    expect(FibonacciMatrixExpo(-3n)).toBe(2n)
+    expect(FibonacciMatrixExpo(-4n)).toBe(-3n)
+    expect(FibonacciMatrixExpo(-5n)).toBe(5n)
+    expect(FibonacciMatrixExpo(-6n)).toBe(-8n)
   })
 })
